These practice algrebra 1 questions are presented with hint on how to solve them. The "Submit" at the bottom of the page will show which questions you answered incorrectly. You may go back to the questions you answered incorrectly and try again.
Q1) The expression $\dfrac{5\sqrt{12}+2\sqrt{27}}{8\sqrt 3}$ simplifies to
A. 0
B. 1
C. 2
D. 3
E. 4
Rewrite $\sqrt{12}$ and $\sqrt{27}$ as follows $\sqrt{12}=\sqrt{4\times3}=\sqrt4\sqrt3=2\sqrt3$ $\sqrt{27}=\sqrt{9\times3}=\sqrt9\sqrt3=3\sqrt3$ Now substitute in the given expression and simplify.
Q2)$-2x^3-x^2+5x-6$ subtracted from $-5x^2+2x-4$ is equal to
A. $2x^3+4x^2+3x+2$
B. $-2x^3+4x^2+3x-2$
C. $-2x^3-6x^2+7x-10$
D. $-2x^3-6x^2-7x-10$
E. $2x^3-4x^2-3x+2$
$A$ subtracted from $B$ is translated mathematically as $B-A$ In the given question $A$ and $B$ are polynomials. Substitute the given polynomials and group like terms.
Q3) If $x=1\dfrac{1}{4}$ and $y=3\dfrac{1}{3}$, then $12x+9y-20=$
A. $-20$
B. $20$
C. $25$
D. $-25$
E. $45$
Note that $1\dfrac{1}{4}=1+\dfrac{1}{4}$ and $1\dfrac{1}{3}=1+\dfrac{1}{3}$
Substitute $x$ by $1+\dfrac{1}{4}$ and $y$ by $1+\dfrac{1}{3}$ in the given expression $12x+9y-20$ and simplify.
Q4) $6x^2-7x-3=$
A. $(6x+1)(x-3)$
B. $(-6x+3)(-x-3)$
C. $(3x-1)(x+3)$
D. $(3x+1)(2x-3)$
E. $(3x-3)(2x+1)$
Two possibilities: 1. Find numbers a,b,c and d such that $(ax+b)(cx+d)=6x^2-7x-3$. 2. You may also expand the possible answers and see which is equivalent to the given expression.
Q5) The operation $■$ is defined by $x ■ y=x^2+3y+2$. If $2■y=-3$, then $y=$
A. $3$
B. $5$
C. $2$
D. $-3$
E. $-4$
Q6) Which of the following is the product of $2$ less than $3$ times $x$ and $2$ more than twice $x$?
A. $6 x^2+2 x-4$
B. $(2-3x)(2x+2)$
C. $6 x^2-2 x+4$
D. $6 x^2$
E. $6 x^3+2 x-4$
Q7) What is the product of the solutions of the equation $-2 x^2=-7$?
A. $\dfrac{2}{7}$
B. $\dfrac{-7}{2}$
C. $7$
D. $2$
E. $0$
Q8) For $x \neq -1$, $\dfrac{2x^2-7x-9}{x+1}=$
A. $2x-9$
B. $x-9$
C. $2x+9$
D. $9-x$
E. $9-2x$
Q9) $x(-2 x+8)(-3 x+1)=$
A. $6 x^3-26 x^2+8 x$
B. $6 x^2-26 x+8 x$
C. $6 x^3+26 x^2+8 x$
D. $6 x^3-26x^2-8 x$
E. $6 x^2+26 x-8$
Q10) $\dfrac{1}{2+\dfrac{2}{x-1}}=$
A. $\dfrac{1}{2 x}$
B. $\dfrac{2}{x-1}$
C. $\dfrac{2 x}{x-1}$
D. $\dfrac{x-1}{2}$
E. $\dfrac{x-1}{2x}$
